63.1.98 problem 145

Internal problem ID [15538]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 145
Date solved : Thursday, October 02, 2025 at 10:19:41 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-8*diff(diff(y(x),x),x)+16*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-2 x} \left (\left (c_4 x +c_3 \right ) {\mathrm e}^{4 x}+c_2 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 35

ode=D[y[x],{x,4}]-8*D[y[x],{x,2}]+16*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-2 x} \left (c_3 e^{4 x}+x \left (c_4 e^{4 x}+c_2\right )+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.055 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*y(x) - 8*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) e^{- 2 x} + \left (C_{3} + C_{4} x\right ) e^{2 x} \]